Surface Tension of Molten Metals I. Copper

588

58PHYSICS: E. E. LIBMAN

PROC. N. A. S.

of the X-ray beam and A is the semi-angle of the cone. This equation gives the form of the longitudinal distribution very satisfactorily. Equations (1) to (3) require, moreover, that the amount of the scattering and, therefore, the space-distribution depend upon both T and Z. The results of Auger given in figure 1 show this to be the case, as do also the results of other observers. Proof of this as well as of the other considerations here presented will be published in detail elsewhere. We conclude, therefore, that the theory of nuclear scattering together with the assumption that the electrons all start from the parent atom in the same direction explains in a satisfactory way all the details of the observed spacedistribution of the photo-electrons ejected by X-rays. 1 Wilson, C. T. R., Proc. Roy. Soc., 104,,1923 (1-24). 2 Auger, P., and C. R., Paris Acad. Sci., 178, 1924 (929-931, 1535-1536); J. Phys. Rad., 8, 1927 (85-92). 3 Bothe, W., Zs. Phys., 26, 1924 (59-73). 4 Bubb, F. W., Phys. Rev., 23, 1924 (137-143). 5 Loughridge, D. H., Ibid., 26, 1925 (697-700); second paper in press. 6 Kirchner, F., Phys. Zs., 27, 1926 (385-389; 799-801). 7 Watson, E. C., in press. 8 Bubb, F. W., Phil. Mag., 49, 1925 (824-838). 9 Bothe, W., Zs. Phys., 26, 1924 (74-84). 10 Auger, P. and Perrin, F., C. R., Paris Acad. Sci., 180, 1925 (1742-1745); Jour. Phys. Rad., 8, 1927 (93-111); Auger, C. R., Paris Acad. Sci., 180, 1925 (1939-1942). 11 Wentzel, G., Zs. Phys., 40, 1926 (574-589). 12 Beck, G., Ibid., 41, 1927 (443-452). 13 Auger, P., J. Phys. Rad., 8, 1927 (85-92). 14 See Rutherford and Chadwick, Phil. Mag., 50, 1925 (889) and references there given. 15 Schonland, B. F. J., Proc. Roy. Soc., 113, 1926 (87-106).

SURFACE TENSION OF MOLTEN METALS. I. COPPER By EARL E. LIBMAN' DBPARTMgNT OF PHYSICS, UNIVZRSITY OF ILLINOIS Communicated June 27, 1927

Except for those that melt at temperatures sufficiently low to allow the use of glass vessels, no accurate data are available concerning the surface tensiofis of the metals. The writer is engaged in determining the capillary constants of the metals that melt above 900°C. and the present paper is an abstract of the work on copper soon to be published in detail as an Engineering Experiment Station Bulletin of the University of Illinois. Theory.-The surface of a liquid in contact with a vertical plane which it does not wet is depressed. The magnitude of this depression h (see Fig. 1) is given by the equation

PHYSICS: E. E. LIBMAN

VOiL. 13, 1927

where

a2

589

h2 = a2(1- sin 0) (1) is the so-called "capillary constant" and is equal to twice the

FIGURE 2

FIGURE 1

FIGURE 3

surface tension divided by the product of the density and the acceleration of gravity. The surface of a liquid within a circular tube of radius r connected to a large reservoir is, if the liquid does not wet the tube, depressed an amount H (see Fig. 1) given by

590

PHYSICS: E. E. LIBMA N

To R¢-mp,s

a'17ad Worm k$ZW'ee/ FIGURE 4

PRoc. N. A. S.

VoL. 13, 1927

rH

a2 C

591

PHYSICS: E. E. LIBMAN

-cos 0

+ C

[ra + {2(a2 a = a2m2/H =

ml2= [rH4

-

m2r2)s/2/3m2r} -2a3/3m2r]/(-cos 0)

(2)2

]rin2j.

We have thus two equations in two unknowns, a2 and 0, and if h and H are known we may calculate a2. Method.-The vertical plane and the tube are combined in a single crucible shown in figures 1 and 2. The metal is melted in this crucible in a high vacuum molybdenum wound furnace. An X-ray picture is taken through the entire furnace and the photograph thus obtained (Fig. 3) is measured. From the measurements of h and H the capillary constant a2 is calculated. The furnace is pictured in figure 4. The furnace is operated at a vacuum which at low heats is about 10-7 mm. of Hg, and at high temperature (about 1400°C.) is never poorer than 10-3 mm. of Hg. The temperature is measured by means of the resistance of the molybdenum furnace winding. The metal at a high red heat is treated with hydrogen to obviate oxidation. During the experiments the metal continually distills, condenses upon the walls and cover of the crucible and runs down again so that the results obtained are for the metal in contact only with its own vapor. The X-ray equipment consists of a Victor universal tube supplied by a large 20 kw. G. E. four-kenotron rectifying set. Applied to Hg, the method gave results for the surface tension ranging from 472 to 480 dynes per cm., which is in good agreement with the literature. The difficulties due to surface contamination by grease at ordinary temperatures, and to which the uncertainty in the published data for mercury is due, are not present at high temperature. Measurements were made from the melting point to 1300°C. on two samples of copper, one of .. great purity and another not so I I I I pure, in order to determine the FIGURE 5 effect of slight contamination. The pure copper was "c.p." material from Baker and Company which, after the experiments, gave on analysis a total of 0.019% of impurities, mostly Fe2O3 and A1203. It was originally in sh;ot form and was melted

411:11111

,.

..

--

-z

l

l

-

l

592

PHYSICS: A. K. BREWER

PROC. N. A. S.'

in an atmosphere of hydrogen to obviate oxidation. A block was cut from the center of a large cylinder thus obtained. The impure sample, analyzed, after the experiments, gave Fe2O3 A120s, 0.07%, SiO2, 0.04%. The results obtained are given below. PURS COPPER TOTAL IMPURITIgS 0.019%

IMPURI COPPBR

TOTAL IMPURITISS 0.11% a2

at

1083 1093 1146 1210 1271 1318

0.308±+ 0.0017 0.308 0.0017 0.304 0.0017 0.305 0.0017 0.304 0.0017 0.297 0.0017.

1083 1097 1110 1160 1195 1220 1335

0.301 0.299 0.315(?) 0.292 0.290 0.287 0.275

The probable error of a2 for the case of pure copper calculated by the method of least squares is 0.0017. Note that the effect of impurities becomes more pronounced as the temperature rises. The results are plotted in figure 5. 1 NATIONAL RZSsARCH FELLOW. 2 See Desains, Ann. chim. phys. (3) 51, 417 (1857).

THE RELATION BETWEEN TEMPERATURE AND WORK FUNCTION IN THERMIONIC EMISSION By A. KrITH BR}WZR1 NORMAN BRIDGE LABORATORY OF PHYSICS, PASADENA

Communicated July 15, 1927

In a recent article in these PROC1VDINGS2 it was shown that some sorts of ionization accompanying chemical action not only followed the Rich-

ardson equation, but possessed such other properties in common with thermionic emission as to suggest that they might be looked upon as special cases of the latter. Under the conditions in which ions were formed at a surface only when chemical action was taking place, distinct relationship was shown to exist between the difference in temperature of emission of the positive and negative ions (6T) and the difference in their work functions (bb) as determined by the usual treatment of an equation of the Richardson form. It is the purpose of the present paper to show that an interdependence also exists between the difference in temperature (8T) and, the difference in work function (bb) for the positive and negative thermionic currents from a given surface in the presence of various gases.